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..."1. I know that you don't set a separate bearing or temperament before tuning, but Scala requires that one start the tuning on one pitch. By default, that pitch is middle C. I'm not sure that's the best place to start. Would A3, the A below A=440, be a better place?"...

Only logically speacking (+ pinch of salt), it should make no difference whether you start from mid-C or another place.

..."2. Does the s1 offset occur at each octave, or does it come at the start of each unit of 24 notes?"...

I do not really know, it may depend on how the S-file expandes the unit, and/or if you can control that. One more trial could be made with 49 notes, wich is the Chas symmetry compass (R-report, section 3.4). There, by taking the semitone 24 as the centre, you gain two 15ths (+ delta, 0-24 and 24-48) and four 12ths (minus-delta). I wish I knew what S-file really needs...

..."(The Scala file that was posted on the PianoTeq site may be fine. I'm just having trouble believing that it was so easy for someone to create and get right the first time.)"...

Good approach, let's believe with a small b...he wrote "I'm impressed by the increase of harmonic resonance you get with this temperament."...but of course, that could be relative...I look forward to hearing some tests and, as you suggest, to analysing in depth.

I read what the on line Pianoteq manual had to say about inharmonicity. I hope it is applied better than it was written about. Phrases something like: So called inharmonicity..., People say that manufacturese want to get rid of all inharmonicity..., and The 33 foot piano would have practically no inharmonicity... Have me wondering how iH is dealt with in the simulation.

If someone could post the frequencies of the 3rd and 4th partials of the As of a tuning I could crunch the numbers and let everyone know how they are dealing with iH.

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Jeff DeutschlePart-Time TunerWho taught the first chicken how to peck?

Hi, Jeff. My impression is that the PianoTeq stretch matches on different partials in different ranges.

Regardless, here are the freqs for the 3rd and 4th partials of the A's for the PianoTeq C3, with the default stretching applied and the temperament set to ET. (One thing: PianoTeq uses Middle C = C3. Thus A3=440. I've retaining that nomenclature below.)

All: I read what the on line Pianoteq manual had to say about inharmonicity. I hope it is applied better than it was written about. Phrases something like: So called inharmonicity..., People say that manufacturese want to get rid of all inharmonicity..., and The 33 foot piano would have practically no inharmonicity... Have me wondering how iH is dealt with in the simulation.

Here is what we wrote in the manual: "A parameter which greatly affects the timbre (and the tuning) is the so-called inharmonicity: the more inharmonic the strings, the more the overtone frequencies of each string are driven away from their theoretical values f, 2f, 3f... and the more the piano sound will resemble a bell. Inharmonicity decreases very rapidly with string length. Experiment by changing the String length. The difference will be most evident in the bass range. You can choose up to a 10 meter long piano! At such a size, there is almost no more inharmonicity. People say that piano manufacturers dreamed of producing pianos without inharmonicity..." (this was a bit of a humoristic touch, being myself piano tuner)

And also:“A unique feature of Pianoteq is that tuning does not follow a pre-computed frequency table (except for the flat temperament), but takes into account the inharmonicity of the strings, in the same way a piano tuner does with acoustic pianos. Hence, the consonance of the notes is improved and the chords have a fuller and richer sound.”

Back to the subject of this thread, I would like to point the fact that for those who want to experiment the CHAS tuning in Pianoteq, they can use SCALA files and load them in Pianoteq, and if the last note in the SCALA file has a value different from 1200.0 (or 2/1), then the inharmonicity will be by-passed and the frequencies will be exactly those specified in the SCALA file. Thus exact experimenting is possible.

Here is how to proceed after creating your own scala file (below an example of an 88 notes scala file content):- tuning section, click on the "mu" microtuning button- import the SCALA file via the "scale" menu - choose "88 notes scale" in the keymap menu

What sort of slope is used for iH in the bass? Does the slope resemble a straight line from note 1 to note 88 on a log graph, or is it somewhat “V” shaped like the iH slope of actual pianos?

Jeff, it is a V with a lower point that can vary depending on the instrument that is modelled. This lower point shifts to the left when you increase the piano size (string length parameter in the interface). For some particular historical instruments, it's more complicate than a V as there are sometimes some sudden discontinuities (broken curve).

I Thank you very much for your involvement and for your help on how to load Chas in Pianoteq.

The opportunity to experiment this temperament can make a great difference, since it may reveal some of this model's qualities and limitations.

Knowing about Pianoteq performances and your experience in piano tuning has been good news for me, as it is not easy to find a reliable device nor someone with both maths and tuning skills.

Chas, as many theoretical models, is meant to translate practical observations and, in this case, what I could experiment throughout my tunings.

About the chance to analyse in depth and share this new approach to the sound scale and its practical effects, I shall welcome any form of collaboration or support that you may be able to offer, at any time.

Hi Alfredo,it's my pleasure if I can help you in some way. If ever you need precise information on the inharmonicity of a particular piano model of Pianoteq to build scala files (knowing that inharmonicity is by-passed in Pianoteq as soon as the last note is not 1200.0), do not hesitate asking me and I will provide you with the values.Cheers,Philippe

Hmm. May be another problem. If iH vanishes when the last note in a Scala file isn't 2x the freq of the first, iH will be turned off in PTeq when CHas is used. That's one of the things that needed testing, if I understand correctly--how the CHas temperament interacts with iH.

If an offset was specified in an 11 freq Scala file, instead of an entry that didn't equal 2X, would PTeq still detect the change on note 12, and shut off iH?

Jake, the iH cant be "shut down'" in my opinion, as it is a composante of the tone. a piano tone without iH may well be unrecognizeable as a piano tone (that would be an interesting test BTW)

To me, what is aborted is the use of the iH correction formula, that allow the intervals as octaves, double,s triples, to have less beats produced by the partials.Philippe tells that it is done "as by a tuner" that mean when listening for an octave the tuner try to have it "beatless" so he tune the top note a little high of the exact 1/2 ratio, so the partials of the top note rub the less with the partials of the lower note. what size of octave daoes it provide I will know in amoment.

We can use the anglo saxon tuners terminology to "name" the octaves in regard of the way the partials are matching.For instance if the 2nd partial of the bottom note match the first partial (funamental) of the top note of the ocatve, the ocatve is said 2:1 , if the octave is ruled an octave above the 4th partial of the bottom note join the second of the top note it is an 4:2 octave, following are 6:3 8:4 10:5 octaves, the concept say that the size (opening) of the octave vary depending of the partial match. It works up to some point, as the result is a coupling of those partials with the coupling of the real 2:1 relation that is also installed in, anyway.

Practically this emphasis the tone of the said partial, which is not always the best thing. The defect of the method is that the partials strenght vary with the voicing, so not the same combination apply in any case, and also the tuner's ear when too much trained to listen in thos high pitched regions, tend to forget to listen more fundamentally, some intervals can be "driven by the noze" in the end...

The same apply when tuning unisons in my opinion : the fundamental couple, and the partials coupling is added to that to open the tone. My usual way to tune unison by regulation of the stabilisation time of the partials install a coupling without listening much to the high partials, but with an assessment of how the energy of the attack is spread and in how much time it stabilize. Those are tactile sensations as well as listening) . But then it is easy to leave whistles in the high regions, with that approach or to have a strong tone which is mostly focused on fundamental strength, closed with lot of energy immediately.

My guess/theory is that if a tuning have a set of relation that use a "natural equilibrium between the partials, this may well contrary the iH of the piano. The strings have iH because of their stiffness, cant they tend to vibe and produce natural harmonics or no ? if so providing them a support or a fundation will help the frequencies to couple toward those (as all the frequencies tend to couple, they dont try to go apart from each other)

Then in the best case, the "natural" tuning would be provided by the center string, the coupling of the external ones taking in account the ih (focusing on the 2-3-4-4 partial match more than on fundamental. When well done the 2outer strings finish at the same exact pitch, while they dont have been tuned together (but each have been tuned to the center string)

This is what can be called "bodying the tone" . As a result, the stabilization of the attack is somehow delayed (later), but the strenght sensation remain, simply a little later. (to my trained ears, I have no idea of the time involved it may count in milliseconds I suppose)

I hope I have made a correct description of an "open" tone.

In theory , this apply, but it is also a somewhat simplist explanation, as the voicin

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It is critical that you call your Senators and Representatives and ask them to cosponsor S. 2587 and H.R. 5052. Getting your legislators to cosponsor these bills

"What sort of slope is used for iH in the bass? Does the slope resemble a straight line from note 1 to note 88 on a log graph, or is it somewhat “V” shaped like the iH slope of actual pianos?

Philippe's: "Jeff, it is a V with a lower point that can vary depending on the instrument that is modelled. This lower point shifts to the left when you increase the piano size (string length parameter in the interface)."...

Today you write:..."That's one of the things that needed testing, if I understand correctly--how the CHas temperament interacts with iH."...

You are exactly on the crucial issue, and I can add only some logical elaborations that lead to more questions.

If the lower point of the iH's slope can shift to the left, depending on the increase of the string's lenth, what will the iH's slope resemble, when using the longest string?

Is the usual iH slope normally referred to 2:1 ratio? What happens when the bass frequencies and consequent strings tension are lowered, like in Chas? Is iH decreased? Should we expect the same frequencies deviation for the high notes?

About approximations: if the string's iH can be decreased (by lowering the bass strings tension and/or increasing the string's length), should we use always the same iH parameter? Should we expect the same iH's slope? The same iH that doubles every 8 semitones? Does not the semitone variate, depending on the incremental ratio?

When do we say "well scaled piano"? Only when we find the usually expected frequencies deviations? Can iH be controlled (spread?), string after string, by playing with string's lengths and diameters (first) and eventually tensions (read frequencies)?

In my comprehension of the thing, when you lower the tension on a given string on agiven piano, you lower the elasticity of the wire, its stiffness raise, hence the iH.

But this is a simplist point of view.

And I suggest that the differnce when tuning with this or that "stretch" is too minimal to be effective at the iH range in an audible way.

I see more resonance quality related to coupling, and harmonic quality related to coherence in beat relations.

In scaling we try to keep the ih at a moderate level at A49 then check the progressivness to avoid jumps. But tension , iH and wire constrain are intimely related, as the fact that the wire may not stretch with too much variability or the piano will loose its tuning more easily with seasonal changes. So in the end for a given sacle lenght not so many choices remain. Certainly some prefer high tension scales and other low tension. iH level will differ in those cases, but stay coherent within the instrument.

The lenght of the strings rule the remaining (but I did not really work on scaling as some that rescale pianos.

When talking with one of the engineer from Bechstein he said to me that there is much more in soundboard, case, and even plate behaviour than in scaling, assuming some basic rules are respected for the latest. the "rescaling trend" make him smile in that regard (but not all pianos have an ideal scale even now) . We can have a few choices with wire style (stiffness and resistance, timbral behaviour)

One of the parameters that relate to iH and that was not much discussed is the wire constrain, or "sollicitation". It can raise to very high levels vs. the breaking limit of the wire, as it lower the iH and provide a better mechanical behaviour (more elasticity), as for Sauter pianos, if I belive in what have been said to me)I suppose that it may relate to soundboard stiffness and impedance, then.Those points are out of my focus by now.

High tension scale may be for instance Fazioli if my basics are good. low tension may be Bechstein.

......

Edited by Kamin (02/27/1006:18 AM)

_________________________
It is critical that you call your Senators and Representatives and ask them to cosponsor S. 2587 and H.R. 5052. Getting your legislators to cosponsor these bills

Isaac, thanks for your remark, I wasn't clear when mentioning that iH would be taken into account or not in Pianoteq. What I meant is that iH will be taken into account or not for the tuning depending on the value of the last note in the scala file. But of course, in all cases, the notes will have their normal iH when played in Pianoteq.

...Practically, [matching partials] emphasizes the tone of the said partial, which is not always the best thing. The defect of the method is that the partials strenght vary with the voicing, so not the same combination apply in any case, and also the tuner's ear when too much trained to listen in thos high pitched regions, tend to forget to listen more fundamentally, some intervals can be "driven by the noze" in the end...

The same apply when tuning unisons in my opinion : the fundamental couple, and the partials coupling is added to that to open the tone. My usual way to tune unison by regulation of the stabilisation time of the partials install a coupling without listening much to the high partials, but with an assessment of how the energy of the attack is spread and in how much time it stabilize. Those are tactile sensations as well as listening) . But then it is easy to leave whistles in the high regions, with that approach or to have a strong tone which is mostly focused on fundamental strength, closed with lot of energy immediately.

My guess/theory is that if a tuning have a set of relation that use a "natural equilibrium between the partials, this may well contrary the iH of the piano. The strings have iH because of their stiffness, cant they tend to vibe and produce natural harmonics or no ? if so providing them a support or a fundation will help the frequencies to couple toward those (as all the frequencies tend to couple, they dont try to go apart from each other)

Then in the best case, the "natural" tuning would be provided by the center string, the coupling of the external ones taking in account the ih (focusing on the 2-3-4-4 partial match more than on fundamental. When well done the 2outer strings finish at the same exact pitch, while they dont have been tuned together (but each have been tuned to the center string)

This is what can be called "bodying the tone" . As a result, the stabilization of the attack is somehow delayed (later), but the strenght sensation remain, simply a little later. (to my trained ears, I have no idea of the time involved it may count in milliseconds I suppose) I hope I have made a correct description of an "open" tone.

May I ask questions about the specifics of the unison tuning for CHas, just to be sure that I understand?

1. Kamin speaks of the unisons not matching on a single partial. How precisely are the outer strings pitched slightly differently to emphasize (through equal beating) specific partials on the center string? One outer string beats equally with partial 1 and 4, for example, and the other beats equally with partial 3 and 6, making the tone evolve towards consonance so that the energy isn't dissipated too fast? In other words, do you listen for these specific beats as you tune the upper unisons? (I understand that they are coupled, also, so that per Weinreich, their interaction in time is actually more complex than I'm acknowledging. I'm just trying to understand the intended pitching of the outer strings as heard during tuning.)

2. How far have people gone in the direction of reducing the "stretch" in tunings and using the raised unisons to reduce the perceived iH? In other words, I can imagine a piano tuned with very little stretch in the upper regions (and CHas has less than some tunings), if the unisons pull the perceived pitch higher by beating with harmonic partials. Are there specific tunings or mistunings or discussions\experiments in this direction that anyone could point me towards? ( I can imagine things like lowering the tension\diapason very slightly and then making the unisons raise the perceived pitch.)

(As an aside: I experimented with pushing that idea a little further one night in PianoTeq, lowering the pitch of some notes past narrowing the octaves, so some notes wavered near flat, and then pushing their unisons up so the notes sounded "in tune." Blame the wine, please. It may be a bad idea, but the sound was not always terrible. Past a certain point, of course, the note just stays flat, but I'm still playing around with this, willing to follow a bad idea to its logical conclusion just to see where the road gets muddy.)

..."May I ask questions about the specifics of the unison tuning for CHas, just to be sure that I understand?

1. Kamin speaks of the unisons not matching on a single partial. How precisely are the outer strings pitched slightly differently to emphasize (through equal beating) specific partials on the center string?"...

I tune the outer strings a little wide. More precisely, while going from wide to the spot, I can hear the partials of the harmonic series. When they reduce in number, I distinguish the point where I hear the 4th, the 3rd and the 2nd.

With my lever, I go anti-clock a little more, so to end charging the pin, then I want the 2nd partial to beam with the foundamental tone of the note I'm unisoning. This, in my experience, gains the longest tone-sustain.

..."2. How far have people gone in the direction of reducing the "stretch" in tunings and using the raised unisons to reduce the perceived iH?"...

I can not answer, I simply do not know.

..."Are there specific tunings or mistunings or discussions\experiments in this direction that anyone could point me towards? ( I can imagine things like lowering the tension\diapason very slightly and then making the unisons raise the perceived pitch.)"...

I do not like raising unisons, unless I find a dead-tone, a bad key with poor sound. No clue about discussions/experiments.

..."I experimented with pushing that idea a little further one night in PianoTeq, lowering the pitch of some notes past narrowing the octaves, so some notes wavered near flat, and then pushing their unisons up so the notes sounded "in tune."...

Also in my experience, mid-register unisons raise the three-chord pich, but when you increase the string's tension you also increase the load onto the bridge, and this effects the nearby piches, especially in the high register.

..."willing to follow a bad idea to its logical conclusion just to see where the road gets muddy."

That is nice, in a way I did the same. When I could not stand anymore my flattening tunings, I left the road my ear would suggest and went for that mud. Today I can gain Chas form only if I tune a wider stretch, the Pre-form.

In another Topic you posted ”I'd better precise: 4ths beat very much in the bass, progressive slowering up to C3 and progressive fastening, going up. At C5 4ths collaps. 5ths go the way you say, "fastest in the middle of the piano and slower to the ends". Actually, at the ends 5ths sound pure, this gives you an idea of how slow they beat, of how little they can be narrow. But in Pre-tuning (centre string), high 5ths get wide.

OK, I seem to have misunderstood the beat rate progression of the 4ths and 5ths when you tune. This makes much more sense. When 4ths get slower, 5ths must get faster and visa versa. And the faster the 4ths are in relation to the 5ths, the wider the octave type. So the progression of 4ths and 5ths indicate the widest octave type at the ends and the narrowest in the middle.

This type of tuning is inconsistent with equal beating 12ths and 15ths which call for a general narrowing of the octave type while going up in the treble. But then, if I understand you correctly, this is the “Chas Preparatory Tuning” which when after the unisons are tuned, produces equal beating 12ths and 15ths. I did make a post a while ago about a possible explanation for how the tuning could change when tuning unison, but since I have never experienced this I am going to continue to consider this to be an “Indulgent Mystery.”

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Jeff DeutschlePart-Time TunerWho taught the first chicken how to peck?

Yes, From the bass up to C3. Here, 4ths get faster and 5ths too continue to get faster up to A3-E4. I'm glad if you get this and I apologize if my English was not correct.

you write:..."This type of tuning is inconsistent with equal beating 12ths and 15ths which call for a general narrowing of the octave type while going up in the treble."...

Actually, Prepare-Chas octaves are S shaped, so 5ths from the bass can go narrower up to mid-range, then invert and go less and less narrow.

..."But then, if I understand you correctly, this is the “Chas Preparatory Tuning” which when after the unisons are tuned, produces equal beating 12ths and 15ths."...

Yes.

..."I did make a post a while ago about a possible explanation for how the tuning could change when tuning unison,"...

Sorry... maybe if I had read that.

..."but since I have never experienced this I am going to continue to consider this to be an “Indulgent Mystery.”"...

Wait Jeff. The "Indulgent Mystery" may be how ET octaves can not be progressive and how ET 12ths and 15ths can routinely (and out of rule) be inverted in the high register, i.e. what has been repeatedly written in Chas main Topic.

Also an "Indulgent Mystery" may be how 4ths and 5ths should be tuned when tempering what ever ET temperament-module, and down C3, where I'm stating that Chas 4ths invert.

Anyway, today I think I was told about quasi-ET, so for me it is not really a mystery anymore. If I may suggest, do experience the Prepare-Tuning.

"S-shaped octaves" do not tell me much. But saying if the fifths become wide of just intonation does. Do the fifths become wide of just intonation or not???? Some of your posts seem to say one thing and some another. If the fifths become just, then the 12ths are wide of just unless only some octaves are narrow which would then mean that it is probably not ET.

And I am the one that gets to choose what I consider to be an "Indulgent Mystery."

_________________________
Jeff DeutschlePart-Time TunerWho taught the first chicken how to peck?

(This is just an aside\interruption, but one that I hope I can make here for the people who are experimenting with Pianoteq. It's available at an academic discount--if you are affiliated with a school or university, there's a different pricing scale. I don't know what the adjustment is. There's a form to fill out at http://www.pianoteq.com/faq?pianoteq=e76fed63871b9bef6603314640867334 . I'm not part of Modartt, by the way. Just a user and fan. The program seems to be a natural match for these discussions. Cheers.)

I'm still trying to learn more about the unison technique. I know that you and Kamin have explained it, and that it has a history. I'm sorry if I seem to be asking the same question several times, but:

1. If the unisons are pitched very slightly higher, so that they have partials that beat equally with partials on the center string, is their fundamental also beating against the fundamental of the center string?

2. Assuming that the answer is yes, is the perceived pitch of the "note" raised to the pitch half-way between the pitch of the center string and the pitches (which may differ) of the unisons? Which means that the perceived pitch emerges from the beating fundamentals and partials of the three strings.

3. Is it thus true to say that, in this method of tuning, there is no one string in the trichord that, if plucked, would be at the same pitch as the pitch heard when all three strings are played together?

4. The 12'ths are slightly flat across the keyboard, if I understand correctly. Should they, after the unisons are tuned in this way, be heard as just? Should some of them, at least, such as above A440?

5.Are the two outer strings usually in unison with one another (as just as possible), or are they pitched to beat with different partials on the center string. Or does this vary, according to the piano and overall tone desired?

I know your questions are to Alfredo and Isaac, but perhaps I can give another view point.

If any one partial of two strings in a unison are at the same frequency, then all the partials of the two strings of the unison are at the same frequency. This is because the strings have the same physical characteristics, and should have the same inharmonicity.

But when two or more strings of a unison are not at the same frequency when played separately, but very close, when they are played together they can "couple" or "pull' each other into vibrating in phase and at the same frequency. This can give a certain color to the tone, especially at the attack when the coupling takes place. And since the piano is really a percussion instrument the mind remembers this color and attributes it to the decay portion of the sound as well.

_________________________
Jeff DeutschlePart-Time TunerWho taught the first chicken how to peck?

You wrote:..."I understand that measurements of frequencies of single strings have been compared to a tuned unison with all three strings sounding together."...

Actually, beats have been compared, not frequencies. I've observed the effects of my unisoning on beats, in different registers.

..."A drop in pitch has been observed."...

Yes, like when you do voicing, in any range. Check yourself: compare a 5th (or an octave), say C5-G5, tune pure on centre strings, then unison and listen to your 5th. Is it still pure?

..."But since a higher partial is measured, I am not sure if it is the fundamental frequency that changes or if it is the effective iH of the strings that change"...

Indeed, when I unison I reinforce the pitch of the centre string. As I've explained, I go for a beam, made up by the mid-string's foundamental and its 2nd partial, gained with the outer strings outcome. In a way, the outer string can syntethize the centre string's pitch, i.e. foundamental + partials. Then, I'd say that both the foundamental frencency and the iH of the strings change.

..."and therefore the frequency of the partials and the beat rate of the tuning intervals."...

It may as well be the strengh/precense of the partials and the overall pitch.

..."This effect is an argument for tuning unisons as you go and for adding a bit of extra stretch when tuning an octave so that when the other strings of the unison are tuned the pitch will settle where it belongs."...

Yes, the pitch has to settle where it belongs, beat-wise.

..."Perhaps this is what you are experiencing rather than the piano’s tension equalizing."...

I talk about piano settlings, considering the sum of those two factors (plus the strings adjustements on their three lenghts). Increasing the string's tension involves the change of loading onto the bridge, maybe very very little but for me and Chas form it is still meaningfull. I need to control unisoning effects on closed notes too.

Fine and coherent voicing solves most problems related to the partials outcome. Thinking of a sound, can coherent timbre proportion the relevance and presence of partials? How would that effect your tuning?